Chem Ch. 11

The energetics of vaporization

- A beakers is open to the atmosphere and thermally insulated so that heat from the surroundings cannot enter the beaker. The molecules that leave the beaker are the ones at the high end of the energy curve: the most energetic. If no additional heat enters the beaker, then the average of the entire collection of molecules decreases; thus, vaporization is an endothermic process, meaning it takes energy to vaporize molecules in a liquid. Vaporization requires overcoming the intermolecular forces that hold liquids together, and since energy is needed to pull the molecules away from one another, the process is endothermic. Our bodies use the vaporization of sweat for cooling. - Condensation, the opposite of vaporization, is exothermic: heat is released when a gas condenses to a liquid. Steam burns are an example of this.

Vapor pressure and dynamic equilibrium

- A flask is sealed and all air has been removed from it, leaving just the liquid. Initially the liquid molecules evaporate, as they would in an open beaker, but, because of the seal, the evaporated molecules can't escape into the atmosphere. As liquid molecules enter the gas state, some start condensing back into the liquid. As the concentration (or partial pressure) of gaseous molecules increases, the rate of condensation also increases. However, as long as the liquid remains at a constant temperature, the rate of evaporation remains constant. Eventually the rate of condensation and vaporization become equal: this is dynamic equilibrium. Condensation and vaporization continue at equal rates and the concentration of water vapor above the liquid is constant. So dynamic equilibrium is when rate of condensation = rate of evaporation. - Thus, the process is as follows: (1) When water is in a sealed container, water molecules begin to vaporize; (2) As water molecules build up in the gas state, they begin to recede into the liquid; (3) When the rate of evaporation equals the rate of condensation, dynamic equilibrium is reached. - Vapor pressure: the pressure of a gas in dynamic equilibrium with its liquid; depends on intermolecular forces present in the liquid as well as temperature. Weak intermolecular forces = volatile substances, high vapor pressures; intermolecular forces are easily overcome by thermal energy. Strong intermolecular forces = nonvolatile substances, low vapor pressures. - A liquid in dynamic equilibrium with its vapor is a balanced system that tends to return to equilibrium if disturbed. When a system in dynamic equilibrium is disturbed, the system response so as to minimize the disturbance and return to state of equilibrium. For example, when volume is increased, pressure falls, so more gas vaporizes and pressure is restored (raised). When volume is decreased, pressure rises, so more gas condenses and pressure is restored (lowered). This is known as Le Chatelier's principle.

The critical point: transition to an unusual state of matter

- A liquid is being vaporized in a sealed container and being heated. As temperature rises, more of the liquid vaporizes and the pressure of the container increases. As the temperature and pressure increase, more and more gas is forced into the same amount of space, and the density of the gas gets higher and higher. At the same time, the increasing temperature causes the density of the liquid to become lower and lower. At a certain high enough temperature, the meniscus between the liquid and gas disappears and the gas and liquid states mix to form a supercritical fluid (neither liquid nor gas). For any substance, the temperature at which this transition occurs is the critical temperate (Tc); the liquid cannot exist (regardless of pressure) above this temperature. The pressure at which this transition occurs is the critical pressure (Pc). - When T < Tc, 2 states (gas and liquid) exist. When T > Tc, one state (supercritical fluid) exists. - A supercritical fluid has properties of both liquids and gases: they can act as good solvents and selectively dissolve a number of compounds. A supercritical fluid can be easily removed by lowering the pressure below the critical pressure.

Navigation within a phase diagram

- At the fusion curve, the temperature stops rising and melting occurs until the solid ice is completely converted to liquid water. Once the ice has been completely melted, the temperature of the liquid water can begin to rise until the vaporization curve is reached. At this point, the temperature again stops rising and boiling occurs until all the liquid is converted to gas. Also at the vaporization curve, the pressure stops dropping and vaporization occurs until all the liquid is completely converted to vapor. Crossing the vaporization curve requires the complete transition from liquid to gas; only after the liquid has all vaporized can the pressure continue to drop. - Change in temperature is represented by a horizontal line. Change in pressure is represented by a vertical line.

Atomic solids

- Atomic solids: solids whose composite units are individual atoms. Can be classified into 3 categories: nonbonding atomic solids, metallic atomic solids, network covalent atomic solids, which are each held together by a different kind of force. - Nonbonding atomic solids: held together by relatively weak dispersion forces, and in order to maximize these interactions, nonbonding atomic solids form closest-packed structures, maximizing their coordination numbers and minimizing the distance between them. Have very low melting points that increase uniformly with molar mass. The only nonbonding atomic solids are noble gases in their solid form. E.g. argon, xenon. - Metallic atomic solids: held together by metallic bonds, which in the simplest model are represented by the interaction of metal cations with the sea of electrons that surround them. Since metallic bonds aren't directional, metals also tend to form closest-packed crystal structures. Have varying strengths. some have melting points below room temperature, while others have high melting points. E.g. gold, iron, mercury, nickel. - Network covalent atomic solids: held together by covalent bonds; the crystal structures of these solids are more restricted by the geometrical constraints of the covalent bonds (which tend to be more directional than intermolecular forces, ionic bonds, or metallic bonds) so they don't tend to form closest-packed structures. Since covalent bonds are very strong, covalent atomic solids have very high melting points; the electrons in covalent atomic solids are confined to the covalent bonds and aren't free to flow, so they typically don't conduct electricity. In diamond, each carbon atom forms 4 covalent bonds to 4 other carbon atoms in a tetrahedral geometry. In graphite, carbon atoms are arranged in sheets; within each sheet, carbon atoms are covalently bonded to each other by a network of sigma and pi bonds; the pi bonds are delocalized over the entire sheet, making graphite a good conductor of electricity. There are no covalent bonds between sheets, only relatively week dispersion forces; consequently, the sheets slide past each other relatively easily, so graphite is a good lubricant. Silicates (extended arrays of silicon and oxygen) are the most common network covalent atomic solids; they compose 90% of Earth's crust; and example is quart and common glass. E.g. diamond, graphite, silicon dioxide.

Crystalline solids and band theory

- Band theory: a model for bonding in solids that is sophisticated and broadly applicable; apples to both metallic solids and covalent solids; atomic orbitals of the atoms within a solid crystal are combined to form orbitals that aren't localized on individual atoms but delocalized over the entire crystal, so the crystal is like a large molecule, and its valence electrons occupy the molecular orbits formed from the atomic orbitals of every atom in the crystal. - As the number of molecular orbitals increase, the spacing between them decreases to so small a value that they're no longer discrete energy levels, but instead form a band of energy levels. One half the orbitals in the band (N/2) are bonding molecular orbitals and (at 0 K) contain the N valence electrons. The other N/2 molecular orbitals are antibonding and (at 0 K) are completely empty. If the atoms composing a solid have p orbitals available, then the same process leads to another band of orbitals at higher energies. - In band theory, electrons become mobile when they transition from the highest occupied molecular orbital into higher energy empty molecular orbitals; thus, we call the occupied molecular orbitals the valence band and the unoccupied orbitals the conduction band. Since the energy difference between orbitals becomes increasingly smaller in atoms with a large number of orbitals, electrons can can easily transition form the valence band to the conduction band. Since electrons in the conduction band are mobile, this makes them a good conductor. Mobile electrons in the conduction band are responsible for the thermal conductivity of metals; when a metal is heated, electrons are excited to higher energy molecular orbital, and these electrons can then quickly transport the thermal energy throughout the crystal lattice. - In metals, the valence band and conduction band are energetically continuous: the energy difference between the top of the valence band and the bottom of the conduction band is irrelevantly small. In semiconductors and insulators, however, an energy gap, called the band gap, exists between the valence and conduction bands. Semiconductors have a small energy gap, but their conductivity can be increased in a controlled way by adding small amounts of other substances, called dopants, to the semiconductor; insulators have a large energy gap, and electrons aren't promoted into the conduction band at ordinary temperatures, resulting in limited conductivity.

Capillary action

- Capillary action: the ability of a liquid to flow against gravity up a narrow tube; the attraction of a liquid's molecules to a surrounding surface (e.g. a glass tube) draws the liquid around the edge of the container up the walls; the rest of the liquid is pulled along by the attraction of the liquid molecules to each other; the narrower the tube, the higher the liquid will rise. - Capillary action is the result of: (1) the attraction between molecules in a liquid (called cohesive forces) and (2) the attraction between these molecules and the surface of the tube (called adhesive forces). Adhesive forces cause the liquid to spread out over the surface of the tube, while the cohesive forces cause the liquid to stay together. If adhesive forces are greater than cohesive forces (like blood in a glass tube), then the attraction to the surface draw the liquid up the tube and the cohesive forces pull along those molecules not in direct contact with the tube walls. The liquid rises up the tube until the force of gravity balances the capillary action: the thinner the tube, the higher the rise. If the adhesive forces are smaller than the cohesive forces (e.g. a thermometer), then the liquid doesn't rise up the tube at all and will drop to a level below the level of the surrounding liquid. - Meniscus: the curved shape of a liquid surface within a tube; concave = rounded inward; convex = rounded outward. A meniscus is concave in liquids that are more strongly attracted to the sides of their container than to each other and convex in liquids that are more strongly attracted to one another than the sides of their container. E.g. water has a concave meniscus, while mercury has a convex one.

Crystalline solids: unit cells and basic structures

- Crystalline lattice: the regular arrangement of atoms within a crystalline solid; nature's way of aggregating particles to minimize their energy. - Unit cell: used to represent the crystalline lattice with a small collection of atoms, ions, or molecules; when repeated over and over, the entire lattice is reproduced. - Lattice point: a point in space occupied by an atom, ion, or molecule. - Many different unit cells exist, but we will classify them by their symmetry, focusing primarily on cubic unit cells. Cubic unit cells are characterized by equal edge lengths and 90° angles at their corners. The 3 cubic unit cells (simple cubic, body-centered cubic, and face-centered cubic) have different characteristics. - Simple cubic: 1 atom per unit cell, coordination number of 6, 2r edge length, 52% packing efficiency. Consists of a cube with 1 atom at each corner; the atoms touch along each edge of the cube. Each corner atom is shared by 8 other unit cells, i.e. any one unit cells actually contains only 1/8 of each of the 8 atoms at its corners, for a total of only 1 atom per unit cell. - Body-centered cubic: 2 atoms per unit cell, coordination number of 8, 4r/square root of 3 edge length, 68% packing efficiency. Consists of a cube with 1 atom at each corner and 1 atom (of the same kind) in the very center of the cube. The atoms don't touch along the edge of the cube, but along the diagonal line that runs from one corner, though the middle of the cube, to the opposite corner. Contains 2 atoms per unit cell because the center atom isn't shared with any other neighboring cells. - Face-centered cubic: 4 atoms per unit cell, coordination number of 12, 2 times square root of 2r edge length, 74% packing efficiency. A cube with 1 atom at each corner and 1 atom (of the same kind) in the center of each cube face. The atoms do not touch along the edge of the cube, but touch along the diagonal face. Contains 4 atoms per unit cell because the center atom on each of the 6 faces are shared between 2 unit cells. So there are a total of 3 face-cetned atoms and 1 (1/8 x 8) corner atoms. - Coordination number: the number of atoms with which each atom is in direct contact; the number of atoms with which a particular atom can strongly interact. - Packing efficiency: the percentage (or fraction) of the volume of the unit cell occupied by the spheres; the higher the coordination number, the greater the packing efficiency.

Crystalline solids: determining their structure and x-ray crystallography

- Crystalline solids are made up of atoms or molecules arranged in structures with long-range order. - X-ray diffraction: a powerful laboratory technique that allows us to study the specific structural pattern of the molecular and atomic scales of crystalline solids and determine the arrangement of atoms and measure the distances between them. - Electromagnetic (or light) waves interact with each other in a characteristic way called interference: they can cancel each other out or reinforce each other depending on the alignment of their crests and troughs. Constructive interference occurs when 2 waves interact with their crests and troughs in alignment. Destructive interference occurs when 2 wave interact with the crest of one aligning with the troughs of the other. - When light encounters 2 slits separated by a distance comparable to the wavelength of light, constructive and destructive interference between the resulting beams produce a characteristic interference pattern of alternating bright and dark lines. - Atoms within crystal structures have spacings between them on the order of 10² pm, so light of similar wavelength forms interference patterns or diffraction patterns when it interacts with those atoms. The exact pattern of diffraction reveals the spacings between planes of atoms. If the difference between the 2 path lengths (2a) is an integral number (n, integral = no fractions) of wavelengths, then the interference will be constructive: nλ = 2a. Using trigonometry we can see that the angle of reflection (θ) is related to the distance (a) and the separation between layers (d). We arrive at the following relationship, known as Bragg's law: nλ = 2d(sin)θ. λ is measured in pm, θ is measured in degrees, and d is measured in pm. - Bragg's law: for a given wavelength of light incident on atoms arranged in layers, we can measure the angle that produces constructive interference (which appears as a bright spot on the X-ray diffraction patter) and then calculate d, the distance between the atomic layers: d = (nλ)/(2sinθ) - In X-ray crystallography, an X-ray beam is passed through a sample, which is rotated to allow diffraction from different crystalline planes. The resulting patterns, representing constructive interference from various planes, are analyzed to determine crystalline structure. X-ray crystallography can also be used to determine the structures of proteins, DNA, and other biological molecules.

Dipole-dipole force

- Dipole-dipole force: exists in all molecules that are polar. Polar molecules have electron-rich regions (which have a partial negative charge) and electron deficient regions (partial positive charge). - On electrostatic potential maps, red = electron-rich, blue = electron-poor. - Permanent dipole: when one region of a molecule is more electron-rich or electron-poor than the other regions because of the different electronegative of the atoms composing the molecule. The positive end of one permeant dipole attracts the negative end of another permanent dipole; this attraction is the dipole-dipole force. Polar molecules, therefore, have higher melting and boiling points than nonpolar molecules of similar molar mass. Since all molecules have dispersion forces, polar masses have dipole-dipole forces in addition to dispersion forces. The additional attractive force raises their melting and boiling points relative to nonpolar molecules of similar molar masses, e.g. formaldehyde (higher) and ethane (lower). - Greater dipole moments = more polarity = higher melting and boiling points. - Miscibility: the ability to mix without separating into 2 states; seen in liquids; partly determined by polarity. Polar liquids are typically miscible with other polar liquids but are not miscible with nonpolar liquids, e.g. water and oil.

Dispersion forces

- Dispersion forces (also called London forces) are present in all molecules/atoms. They are the result of fluctuations in electron distribution within molecules/atoms. Since all atoms and molecules have electrons, they all exhibit dispersion forces. The electrons in an atom or molecule may, at any one instant, be unevenly distributed. Electrons at one point in time may not be symmetrically arranged around the nucleus, meaning one side has a slightly negative charge (more electrons) and the other side has a slightly positive charge (less electrons); this fleeting charge separation is called an instantaneous dipole or a temporary dipole. An instantaneous dipole on one atom induces an instantaneous dipole on the neighboring atoms because the positive end of the instantaneous attracts electrons in the neighboring atoms. The neighboring atoms then attract one another (positive to negative ends on neighboring atoms). This attraction is the dispersion force. - The magnitude of the dispersion force depends on how easily the electrons in the atom or molecule can move or polarize in response to an instantaneous dipole, which in turn depends on the size (or volume) of the electron cloud. A larger electron cloud results in a greater dispersion force because the electrons are held less tightly by the nucleus and there polarize more easily. If all other variables are constant, the dispersion force increases with increasing molar mass because molecules/atoms of higher molar mass generally have more electrons dispersed over a great volume. As molar masses and electron cloud volumes increase, the greater dispersion forces result in increasing boiling points (because the molecules are more strongly attracted to one another). - Shape also determines the magnitude of dispersion forces. Long molecules, which can interact with one another along their entire length, have lower boiling points than bulky, round molecules that have a smaller area of interaction between neighboring molecules.

Summarizing intermolecular forces (in order of increasing strength)

- Dispersion forces are present in all molecules/atoms and increase with increasing molar mass. These forces are always weak in small molecules but can be significant in molecules with high molar masses. - Dipole-dipole forces are present in polar molecules. - Hydrogen bonds, the strongest of the intermolecular forces that can occur in pure substances (second only to ion-dipole forces in general) are present in molecules containing hydrogen bonding directly to fluorine, oxygen, or nitrogen. - Ion-dipole forces are present in mixtures of ionic compounds and polar compounds. These forces are very strong and are especially important in aqueous solutions of ionic compounds.

Doping: controlling the conductivity of semiconductors

- Doped semiconductors contain small amounts of impurities that result in additional electrons in the conduction band or electron "holes" in the valence band. - The atoms from the group 5 Adoping element (phosphorous is one that is used) are incorporated into the semiconductor's crystal structure, and deac hoping atom brings with it one additional electron. The additional electrons go into the conduction band if the valence bond is completely full; these electrons are then mobile and can conduct electrical current. This type of semiconductor is called an n-type semiconductor because the charge carriers are negatively charged electrons in the conduction band. - When doped with a 3A element (e.g. gallium), the doping element is incorporated into the crystal structure and results in electron "holes", or empty molecular orbitals, in the valence band. This presence of holes allows for the movement of electrical current because electrons in the valence band can move between the holes. In this way, the holes move in the opposite direction as the electrons. This type of semiconductors is called a p-type semiconductor because each hole acts as a positive charge. - P-n junctions: tiny spots that are p-type on one side and n-type on the other. These junctions can act as diodes (circuit elements that allow the flow of electrical current in only one direction) or amplifies (elements that amplify a small electrical current into a larger one) among other things.

Sublimation

- Even in a solid the molecules have thermal energy, which causes each one to vibrate about a fixed point. The motion is much less vigorous than in a liquid, but it's still significant. As in liquids, at any instant some molecules in the block of ice have more thermal energy than the average and some have less. The molecules with high enough thermal energy can break free from the solid surface (whereas in liquids, molecules are held less tightly than in the interior due to fewer neighbor-neighbor interactions) and go directly into the gas state; this process of solid to gas is called sublimation. - Some of the molecules in the gas state (those at the low end of the energy distribution curve for the gaseous molecules) collide with the surface of these solid and are captured by the intermolecular forces with other molecules; this process of gas to solid is the opposite of sublimation and is called deposition. The pressure of gas in dynamic equilibrium with its solid the vapor pressure of the solid. - Both sublimation and deposition can occur on the surface of a solid exposed to the atmosphere at a certain temperature, but sublimation usually occurs at a greater rate because most of the newly sublimed molecules escape into the surrounding atmosphere and never come back meaning there's a noticeable decrease in the size of solid over time. - Ice shrinking in the freezer (even though it stays below 0°C) is an example of sublimation, so is freezer burn and dehydration of frozen foods. Dry ice is commonly associated with sublimation, and it never melts under atmospheric pressure no matter the temperature.

Heat of vaporization

- Heat (or enthalpy) of vaporization (ΔHvap): the amount of heat needed to vaporize one mole of a liquid to gas. The heat of vaporization of water at 100°C is +40.7 kJ/mol: H₂O(l) ↔ H₂O(g), ΔHvap = +40.7 kJ/mol. - The heat of vaporization is always positive because the process is endothermic: energy must be absorbed to vaporize a substance. The heat of vaporization is somewhat temperature dependent, for example heat of vaporization slightly increases (becomes more positive) when the temperature is lowered. - When a substance condenses from a gas to a liquid, the same amount of heat is involved, but the heat is emitted rather than absorbed: H₂O(g) ↔ H₂O(l), ΔH = -ΔHvap = -40.7 kJ/mol. - When one mole of water condenses, it releases 40.7 kJ of heat. The sign of ΔH in this case is negative because the process is exothermic. - The heat of vaporization can be used to calculate the amount of energy needed to vaporize a given mass of liquid (or the amount of heat given off by the condensation of a given mass of liquid). The heat of vaporization is like a conversion factor between # of moles of liquid and the amount of heat required to vaporize it (or the amount of heat emitted when it condenses). See page 502.

Closest-packed structures

- In metals bond aren't usually directional, so it's helpful to think of crystal structures with the atoms stacking in layers. Think of it as one layer of atoms arranged in a square pattern with the next layer stacking directly over the first so that the atoms in one layer align exactly on top of the atoms in the layer beneath it. - Crystal structures have a great deal of empty space. More space-efficient packing can be achieved by aligning neighboring rows of atoms in a patter with one row offset form the next by one-half a sphere. In this way, the atoms pack more closely to each other in any one layer. - We can further increase the packing efficiency by placing the next layer not directly on top of the first but again offset so that any one atom actually sits in the indentation formed by 3 atoms in the layer beneath it. This kind of packing leads to 2 different crystal structures called closest-packed structures, both of which have packing efficiency of 74% and a coordination number of 12. - In the first of these 2 closest-packed structures, called hexagonal closest packing, the third layer of atoms aligns exactly on top of the first. The pattern from one layer to the next is ABAB, with the third layer aligning exactly above the first. The central atom in layer B is touching 6 atoms of its own layer, 3 atoms of the layer above it, and 3 atoms of the layer below it, for a total coordination number of 12. The unit cell for this structure is not cubic but hexagonal. - The second of these 2 closest-packed structures, called cubic closest packing, has a third layer of atoms offset from the first, so the pattern from one layer to the next is ABCABC, with every fourth layer aligning with the first. The unit cell for the cubic closes packing is the face-centered bric cell; the 2 have identical structures.

Fusion

- Increasing thermal energy causes liquid molecules to vibrate faster and faster. At the melting point of the liquid, the molecules have enough thermal energy to overcome the intermolecular forces that hold the molecules at their stationary points, and the solid turns into a liquid; this process of the transition from solid to liquid is called melting or fusion (the term fusion is used because if we heat several crystals of a solid, they fuse into a continuous liquid upon melting). The opposite of melting is freezing, the transition from liquid to solid. - Once the melting point of a solid is reached, additional heating only causes more rapid melting; it doesn't raise the temperature of the solid above its melting point. Only after all the solid has melted will additional heating raise the temperate of the liquid past its melting point. A mixture of solid and liquid is always equal to the melting point.

Ion-dipole force

- Ion-dipole force: occurs when an ionic compound is mixed with a polar compound. Stronger than dispersion and dipole-dipole forces and hydrogen bonds. Ion-dipole forces are the strongest of they intermolecular forces and are responsible for the ability of ionic substances to form solutions with water. - E.g. NaCl mixed with H₂O, causing the sodium and chloride ions to interact with water molecules via ion-dipole forces. The positive sodium ions interact with the negative poles of water molecules, while the negative chloride ions interact with the positive poles.

Ionic solids

- Ionic solids: solids whos composite units are ions; held together by coulombic interactions between the cations and anions occupying the lattice sites in the crystal. - The coordination number of the unit cell for an ionic compound represents the number of close cation-anion interactions. Since these interactions lower potential energy, the crystal structure of a particular ionic compound is the one that maximizes the coordination number while accommodating both charge neutrality (each unit cell must be charge neutral) and the different sizes of the cations and anions that compose the particular compound. Generally, the more similar the radii of the cation and the anion, the higher the coordination number. - A cesium chloride unit cell, for example, is a simple cubic cell, with one cesium ion lying in the very center of the cell. So, the cesium chloride unit cell will contain one chloride anion (1/8 x 8 = 1) and one cesium cation for a ration of Cs to Cl of 1:1, as the molecular formulate indicates. - Charge neutrality requires that each cation be surrounded by an equal number of anions. - With more disproportionally sized ions, high coordination numbers are physically impossible. - Tetrahedral hole: the empty space that lies in the center of a tetrahedral arrangement of 4 atoms, such as ZnS. - When the ratio of cations to anions is not 1:1, the crystal structure must accommodate the unequal number of cations and anions. Compounds with anion to cation ratio of 2:1 often exhibit the fluorite structure; compounds with a cation to anion ratio of 2:1 often exhibit the antifluorite structure. The ion that has the greater amount in the compound occupies the tetrahedral holes beneath each corner atom and the one with less occupies the lattice sites of a face-centered atom. - E.g. NaCl, CsCl, ZnS, and CaF₂

Surface tension

- Manifestations of intermolecular forces in liquids: surface tension, viscosity, and capillary action. - Surface tension: the tendency of liquids to minimize their surface area. Molecules at the liquid surface have a higher potential energy than those in the interior. As a result, a liquid tends to minimize its surface area. Interactions between molecules lower their potential energy in a way similar to how the interactions between protons and electrons lower their potential energy, in accordance with Coulomb's law. - A molecule at the surface of a liquid has fewer neighbors than a molecule in the interior. With less neighbors to interact with, molecules at the surface are inherently less stable (have higher potential energy) than those on the interior. In order to increase surface area, molecules from the interior have to be moved to the surface, and, because molecules at the surface have higher potential energy than those on the interior, this movement requires energy. Therefore, liquids tend to minimize their surface area. - Surface tension: the energy required to increase the surface area by a unit amount, e.g. water has a surface tension of 72.8 mJ/m², meaning it takes 72. mJ to increase the surface area of water by 1 square inch. - The tendency of liquids to minimize their surface creates a kind of skin at the surface that resists penetration; if something tries to penetrate the water's surface, the water's surface area must increase slightly, and this change is resisted by the surface tension. When the necessary energy is provided, an object can overcome the surface tension. - Surface tension decreases as intermolecular forces decrease (and increase as intermolecular forces increase). - Surface tension is the reason water droplets form nearly perfect spheres; a sphere is the geometrical shape with the smallest surface area to volume ratio, so the formation of a sphere minimizes the number of molecules at the surface, thus minimizing the potential energy of the system.

Introduction

- Matter exists mainly in 3 states: solid, liquid, and gas. The solid and liquid states are known as the condensed states and are more similar to each other than they are to the gas state. In the gas state, atoms or molecules are separated by large distances and don't interact with each other very much. In condensed states, atoms and molecules are close together and exert moderate to strong attractive forces on one another. - Intermolecular forces: attractive forces that exist between molecules and atoms; hold many liquids and solids together. All living organisms depend on intermolecular forces for physical and physiological processes. The state of a sample of matter depends on the magnitude of intermolecular forces between its atoms or molecules and the amount of thermal energy in the sample. - Molecules and atoms that make up matter are in constant random motion that increase with increasing temperature. The energy associated with this motion is thermal energy. When thermal energy is higher than intermolecular forces, matter tends to be gaseous. When thermal energy is lower than intermolecular forces, then matter tends to be liquid or solid.

Energetics of melting and freezing

- Melting is endothermic: solids absorb heat from the more energetic liquids. - Heat of fusion (ΔHfus): the amount of heat required to melt 1 mol of a solid. The heat of fusion for water is 6.02 kJ/mol: H₂O(s) ↔ H₂O(l), ΔHfus = 6.02 kJ/mol - The heat of fusion is positive because melting is endothermic. Freezing, the opposite of melting is exothermic because heat is released when a liquid freezes into a solid. The change in enthalpy for freezing has the same magnitude as the heat of fusion but the opposite sign: H₂O(l) ↔ H₂O(s), ΔH = -ΔHfus = -6.02 kJ/mol. - Different substances have different heats of fusion. Generally, the heat of fusion is much less than its heat of vaporization. The solid and liquid states are closer to each other than they are to the gas state, so it takes less energy to melt 1 mol of ice into liquid than it does to vaporize 1 mol of liquid water into gas because vaporization requires complete separation of molecules from one another, so the intermolecular forces must be completely overcome. Melting, however, requires that intermolecular forces be only partially overcome, allowing molecules to move around one another while still remaining in contact.

Molecular solids

- Molecular solids: solids whose composite until are molecules; lattice sites are occupied by molecules; held together by intermolecular forces (e.g. dispersion and dipole-dipole forces, hydrogen bonds); tend to have low to moderately low melting points, however strong intermolecular forces (such as hydrogen bonds in water) can increase the melting points of some molecular solids. - E.g. ice and dry ice.

Hydrogen bonding

- Polar molecules containing hydrogen atoms bonded direclty to small electronegative atoms (namely fluorine, oxygen, or nitrogen) exhibit an intermolecular force called hydrogen bonding. E.g. H₂O, HF, and NH₃. - Hydrogen bonding is sort of super dipole-dipole force because the large electronegativity difference between hydrogen and these small electronegative elements causes the hydrogen atom to have a fairly large partial positive charge within the bond, while the F, O, or N has a fairly large partial negative charge. Furthermore, since these atoms are all quite small, the H atom on one molecule can approach the F, O, or N atom on an adjacent molecule very closely, resulting in a strong attraction between the H atom on one molecule and the F, O, or N on its neighbor; this is a hydrogen bond. - Hydrogen bonds shouldn't be confused with chemical bond. Chemical bonds occur between individual atoms within a molecule (intramolecular forces), while hydrogen bonds, like dispersion forces and dipole-dipole forces, are intermolecular forces that occur between molecules. Hydrogen bonds are about 2-5% as strong as a covalent bond, but they are stronger than dispersion and dipole-dipole forces. Substances composed of molecules with hydrogen bonds have high melting and boiling points. - Without hydrogen bonding, our entire planet would be gaseous. Because of hydrogen bonding, the boiling point of water is larger than expected when compared to other hydrogen-containing compounds that don't form hydrogen bonds. - Base pairs of nucleotides in DNA are joined by hydrogen bonds.

Crystalline solids: the fundamental types

- Solids may be crystalline (comprising a well-ordered array of atoms or molecules) or amorphous (having no long-range order). Crystalline solids can be classified into 3 categories: molecular, ionic, and atomic, based on the individual units that compose these solids. - Atomic solids can be classified further into 3 categories depending on the types of interactions between atoms within the solid: nonbonded, metal, and network covalent. - Molecular solids: composite units are molecules; low melting points. - Ionic solids: composite units are formular units (cations and anions); high melting points. - Atomic solids: composite units are atoms; divided into nonbonding, metallic, and network covalent. - Nonbonding: held together by dispersion forces; low melting points. - Metallic: held together by metallic bonds; variable melting points. - Network covalent: held together by covalent bonds; high melting points.

Solids, liquids, and gases

- The densities of water in its solid and liquid state are much greater than the density of water in its gas state. The solid and liquid states of water are also more similar in density and molar volume to each other than they are to the gas state. The molecules in liquid and solid water are in close contact with one another (essentially touching) while those in gaseous water are separated by large distances. - For water, the density of the solid is slightly less than the liquid; this is atypical behavior. Most solids are slightly denser than their corresponding liquids because the molecules move closer together upon freezing. - Even though atoms/molecules in a liquid are in close contact, thermal energy partially overcomes the attractions between them, allowing them to move around one another. This isn't the case in solids; the atoms or molecules in a solid are virtually locked in their positions, only vibrating back and forth about a fixed point. - Liquids assume the shape of their container because the atoms/molecules are free to flow (i.e. move around each other). Liquids aren't easily compressed because the molecules/atoms are already in close contact: they can't be pushed much closer together. the molecules in a gas, on the other hand, have a lot of space between them and are easily forced into a smaller volume by an increase in external pressure. - Solids have a definite shape because the molecules/atoms are fixed in place: each molecule or atom merely vibrates about a fixed point. Liquids and solids have definite volume and generally can't be compressed because the molecules/atoms are in close contact. - Solids may be crystalline, which means the atoms/molecules are arranged in a well-ordered 3-D array. They can also be amorphous, which means the atoms/molecules have no long-range order. - Gas: low density, indefinite shape, indefinite volume, weak intermolecular forces. - Liquid: high density, indefinite shape, definite volume, moderate intermolecular forces. - Solid: high density, definite shape, definite volume, strong intermolecular forces.

The major features of a phase diagrams

- The state of a substance changes with temperature and pressure. We can combine both temperature dependence and pressure dependence of the substance in a graph called a phase diagram. - Phase diagram: a map of the state or phase of a substance as a function of pressure (y-axis, in torr) and temperature (x-axis, °C). - We categorize the main features of the phase diagram as regions, lines, and points. - Regions: Any of the 3 main regions (solid, liquid, gas) in the phase diagram represent conditions where that particular state is stable, i.e. under any of the temperatures and pressures within the liquid region in the phase diagram of water, the liquid is the stable state. In general, low temperatures and high pressures favor the solid state, high temperatures and low pressures favor the gas state, and intermediate conditions favor the liquid state. A sample of matter that's not in the state indicated by its phase diagram for a given set of conditions converts to that state when those conditions are imposed, e.g. steam that is cooled to room temperature at 1 atm condenses to liquid. - Lines: Each of the lines (or curves) in the phase diagram represents a set of temperatures and pressures at which the substance is in equilibrium between the 2 states on either side of the line. The line between liquids and gas is called the vaporization curve; the line between the solids and liquids is called the fusion curve; and the line between the solids and gases is called the sublimation curve. At any of the temperatures and pressures along these curves, the 2 states are equally stable and in equilibrium. - The triple point: The triple point represents the unique set of conditions at which the 3 states are equally stable and in equilibrium. Under these unique conditions, the solid, liquid, and gas states are equally stable and will coexist in equilibrium. - The critical point: At the critical temperature and pressure, the liquid and gas states coalesce into a supercritical fluid. The critical point in a phase diagram represents the temperature and pressure above which a supercritical fluid exists.

Intermolecular foces: the forces that hold condensed states together

- The structure of the particles that compose a substance determine the strength of the intermolecular forces that hold the substance together, which thus determines whether the substance is a solid, liquid, or gas at a give temperature. At room temperature, moderate to strong intermolecular forces tend to result in solids or liquids (high melting and boiling points), while weak intermolecular forces tend to result in gases (low melting and boiling points). - Intermolecular forces arise from the interaction between charges, partial charges, and temporary charges on molecules/atoms/ions. - Coulomb's Law: the potential energy (E) of 2 oppositely charged particles (with charges q₁ and q₂) decreases (becomes more negative) with increasing magnitude of charge and with decreasing separation (r): E = (1/4πε₀) ∙ (q₁q₂/r). When q₁ and q₂ are opposite in sign, E is negative. - Thus, protons and electrons are attracted to each other because their potential energy decreases as they get closer together. Similarly, molecules with partial or temporary charges are attracted to each other because their potential energy decreases as they get closer together. However, intermolecular forces, even the strongest ones, are generally much weaker than bonding forces. - The weakness of intermolecular forces compared to bonding forces is because bonding forces are the result of large charges (the charges on protons and electrons) interacting at very close distances, while intermolecular forces are the result of smaller charges interacting at greater distances. The length of the bonds between molecules is longer, and the larger distances as well as the smaller charges involved result in weaker forces. - Types of intermolecular forces: dispersion forces, dipole-dipole forces, hydrogen bonding, and ion-dipole forces. The first 3 of these can potentially occur in all substances, while the last only occurs in mixtures.

The Clausius-Clapeyron equation

- The vapor pressure of a liquid increases with with increasing temperature; however, the relationship isn't linear. Doubling the temperature results in more than a doubling of the vapor pressure. The relationship between vapor pressure and temperature is exponential. - Clausius-Clapeyron: ln Pvap = [(-ΔHvap/R) ∙ (1/T)] + ln β. - Pvap is the vapor pressure, β is a constant that depends on the gas, ΔHvap is the heat of vaporization, R is the gas constant (8.314 J/mol ∙ K), and T is the temperature in kelvins. - The Clausius-Clapeyron equation mirrors the format of the slope of line. ln Pvap is equal to y, (1/T) is equal to x, ln β is the y-intercept, and (-ΔHvap/R) is the slope . - The Clausius-Clapeyron equation gives a linear relationship, not between the vapor pressure and temperature (which have an exponential relationship), but between the natural log of the vapor pressure and the inverse of the temperature. This equation lets of measure the heat of vaporization in a laboratory by simply measuring the vapor pressure of liquid as a function of temperature and then creating a plot of the natural log of the vapor pressure v.s. the inverse of the temperature. We can then determine the slop of the line to find the heat of vaporization. Plug in the slope of the line to ΔHvap in (-ΔHvap/R) to get the heat of vaporization in kJ/mol. - The Clausius-Clapeyron equation ignores the small amount of temperature dependence of ΔHvap. - The Clausius-Clapeyron equation can also be expressed in a two-point form, which needs just 2 measurements of vapor pressure and temperature to determine the heat of vaporization: ln(P2/P1) = (-ΔHvap/R) ∙ [(1/T₂) - (1/T₁)]. We can use this equation to predict the vapor pressure of a liquid at any temperature if we know the enthalpy of vaporization and the normal boiling point (or vapor pressure at some other temperature). If P₁ is not given, it is usually 760 torr. To solve for P₂, remember that ln P₂/P₁ = x becomes P₂/P₁ = e^x is equivalent to P₂ = P₁ ∙ (e^x). - T is in kelvins. ΔHvap is in kJ/mol (should convert to J/mol). R is 8.314 J/mol ∙ K. P is in torr.

Heating curve for water

- The y-axis of a heating curve represents the temperature (°C) of the water sample. The x-axis represents the amount of heat added (in kilojoules/mol) during heating. - The process of heating can be divided into 5 segments: (1) ice warming, (2) ice melting into liquid water, (3) liquid water warming, (4) liquid water vaporizing into steam, and (5) steam warming. - In segments 2 and 4, the temperature is constant as heat is added because the added heat goes into producing the transition between states, not to increasing the temperature. The 2 states are in equilibrium during the transition and the temperature remains constant. The amount of heat needed to achieve state change is given by q = nΔH. - In segments 1, 3, and 5, temperature increases linearly. These segments represent the heating of a single state in which the deposited heat raises the temperature in accordance with the substance's that capacity (q = m∙Cs∙ΔT). (1) Warming of solid ice (to 0°C). No transition between states occurs here, so the amount of heat needed to heat the solid ice is given by q = m∙Cs∙ΔT, where Cs (in J / g∙°C) is the specific heat capacity of ice. ΔT = final temperature - initial temperature. (2) Water is transitioning from solid to liquid. Added heat doesn't change the temperature of the ice and water mixture because heat is absorbed by the transition between states. The amount of heat needed to convert the ice to liquid water is given by q = nΔHfus, where n is the number of moles of water and ΔHfus is the heat of fusion. (3) Liquid water is warmed from 0°C to 100°C. No transition between states occurs, so q = m∙Cs∙ΔT is used to calculate the amount of heat required to heat the liquid. The heat capacity of liquid water (not ice) is now used. (4) Water transitions from a liquid to gas. The amount of heat needed to convert the liquid to gas is give by q = nΔHvap, where n is the number of moles and ΔHvap is the heat of vaporization (kJ/mol). Temperature doesn't change in this segment; the liquid and gas coexist at 100°C as the boiling occurs and water is vaporizing into steam. (5) Steam is warmed above 100°C. No transition between states occurs, so the amount of heat needed to heat the steam is given by q = m∙Cs∙ΔT. We must use the specific heat capacity of steam.

The phase diagrams of other substances

- Unlike for water, the fusion curves for iodine and carbon dioxide have positive slopes (i.e. as temperature increases, pressure also increases); the behavior of water is atypical. The fusion curve for most substances has a positive slope because increasing pressure favors the denser state, which for most substances is the solid state. Unlike most substances, the liquid state of water is denser than its solid state. - Carbon dioxide, unlike water and iodine, has no stable liquid state at 1 atm; the sublimation curve is crossed before this point, so the solid sublimes to a gas (e.g. dry ice). CO₂ will only form a liquid above pressures of 5.1 atm. - If a pressure is below the triple point, then the liquid state is not stable. Thus, if a solid is warmed at a pressure below the triple point, then it will sublime from a solid to a gas.

The process of vaporization

- Vaporization: the process by which thermal energy can overcome intermolecular forces and produce a state change from liquid to gas. Some molecules in an open beaker have enough kinetic energy to vaporize from the surface of the liquid. - Liquid molecules in a beaker at room temperature open to the atmosphere. The molecules are in constant motion because of thermal energy; the higher the temperature, the greater the average energy of the collection of molecules. However, at any one time, some molecules have more thermal energy than average and some have less. - The distributions of thermal energies for the molecules in a sample of a liquid at 2 different temperatures show that some molecules (at the high end of the distribution curve) have enough energy to break free from the surface (where molecules are held less tightly than in the interior due to fewer neighbor-neighbor interactions) and into the gas state. This transition from liquid to gas is called vaporization. Some of the liquid molecules in the gas state at the low end of the energy distribution curve for the gaseous molecules plunge back into the water and are captured by intermolecular forces; this transition, from gas to liquid, is the opposite of vaporization and called condensation. - Evaporation occurs at a greater rate in a container open to the atmosphere because most of the newly evaporated molecules escape into the surrounding atmosphere and never come back; the result is a noticeable decrease of the liquid over several days. - When temperature increases, more molecules have enough energy to break free and evaporate, so vaporization occurs more quickly. - Molecules at the surface have a greater tendency to evaporate because they're held less tightly, so as surface area increase, vaporization also increases. - Weaker intermolecular forces allow more molecules to evaporate at a given temperature, increasing the rate of vaporization. We call liquids that vaporize easily volatile (e.g. acetone), and those that don't vaporize easily nonvolatile (e.g. motor oil). - Summarize: The rate of vaporization increases with increasing temperature. The rate of vaporization increase with increasing surface area. The rate of vaporization increases with decreasing strength of intermolecular forces.

Viscosity

- Viscosity: the resistance of a liquid to flow; measured in poise (P), which is defined as 1 g/cm ∙ s. The viscosity of water at room temperate is about one centipoise (cP). - Viscosity is greater in substances with stronger intermolecular forces because if molecules are more strongly attracted to each other, they don't flow around each other as freely. - Viscosity also depends on molecular shape, increasing in longer molecules that can interact over a greater area and possibly become entangled. - As mass increases (and therefore dispersion forces increase) or molecular length increases, viscosity increases. - Viscosity also depends on temperature because thermal energy partially overcomes the intermolecular forces, allowing molecules to flow past each other more easily. Thus, as temperature increases, viscosity decreases.

Water

- Water is the most common and important liquid on Earth. The majority of our body mass is water. Life as we know it is impossible without water and its unique properties. - Water has a low molar mass, yet it's a liquid at room temperature. No other substance of similar molar mass come close to being a liquid at room temperature (except for HF). Water is the only common main-group hydride that is a liquid at room temperature. Water has a high boiling point yet a low molar mass because of its highly polar nature (has a significant dipole moment) and 2 O-H bonds that allow it form strong hydrogen bonds with 4 other water molecules. Water's high polarity also allows it to dissolve many substances (polar and ionic ones) and even a number of of polar gases by inducing a dipole moment in their molecules. Water is the main solvent of living organisms and the environment. - Water has an abnormally high specific heat capacity, which has a moderating effect on temperatures of coastal cities and the world at large. - The way water freezes is also unique. Unlike other substances, which contract upon freezing, water expands upon freezing. Consequently, ice is less dense than liquid water, which is why ice floats.

Changes between states

- We can transform one state of matter to another by changing the temperature, pressure, or both. In general, increase in pressure favor the denser state, so increasing the pressure of a gas sample results in a transition to a liquid state. - Solid to liquid: heat. Liquid to solid: cool. - Liquid to gas: heat or reduce pressure. Gas to liquid: cool or increase pressure.

Temperature dependence of vapor pressure and boiling point

- When the temperature of a liquid increases, its vapor pressure rises because the higher thermal energy increases the number of molecules that have high enough energy to vaporize. Because of the thermal energy distribution curve's shape, a small change in temperature makes a large difference in the number of molecules with enough energy to vaporize, which results in a large increase in vapor pressure. E.g. at 60°C, the vapor pressure of water is about 200 torr, while at 100°C the vapor pressure is 760 torr. - Boiling point: the temperature at which a liquid's vapor pressure equals the external pressure. When a liquid reaches its boiling point, the thermal energy is enough for molecules in the interior to break free of their neighbors and enter the gas state. - Normal boiling point: the temperature at which a liquid's vapor pressure equals 1 atm. The normal boiling point of pure water is 100°C. However, at a lower pressure, water boils at a lower temperature, e.g. in Colorado, water boils at 94°C, which makes food take longer to cook. - A liquid boils when thermal energy is high enough to cause molecules in the interior of the liquid to become gaseous, forming bubbles that rise to the surface. Once the boiling point of a liquid is reached, additional heating only causes more rapid boiling: it doesn't raise the temperature of the liquid above the boiling point, as seen in a heating curve. Therefore, at 1 atm, boiling water always has a temperature of 100°C. As long as liquid water is present, its temperature can't rise above the boiling point; however, once all the water has been converted to steam, the temperature of the steam can continue to rise beyond 100°C.